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On the topological features of optimal metabolic pathway regimes

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Abstract

In this work, the stoichiometric metabolic network ofEscherichia coli has been formulated as a comprehensive mathematical programming model, with a view to identifying the optimal redirection of metabolic fluxes so that the yield of particular metabolites is maximized. Computation and analysis has shown that the over-production of a given metabolite at various cell growth rates is only possible for a finite ordered set of metabolic structures which, in addition, are metabolite-specific. Each regime has distinct topological features, although the actual flux values differ. Application of the model to the production of 20 amino acids on four carbon sources (glucose, glycerol, lactate, and citrate) has also indicated that, for fixed cell composition, the maximum amino acid yield decreases linearly with increasing cell growth rate. However, when the cell composition varies with cell growth rate, the amino-acid yield varies in a nonlinear manner. Medium optimization studies have also demonstrated that, of the above substrates, glucose and glycerol are the most efficient from the energetic viewpoint. Finally, model predictions are analyzed in the light of experimental data.

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Abbreviations

b :

vector of net conversion rates, T-1

C :

time required to replicate the chromosome, T

Cp :

peptide elongation rate, LT-1

D :

time period between termination of a round of replication and the following cell division, T

Di :

drain factor of metabolite,i,T -1

(Ds/rx)gr :

growth related dissipation of Gibbs energy, L2T-2

fai :

amount of amino acid,ai, needed for biomass formation, M

Ji :

reaction flux, T-1

me :

maintenance related dissipation of Gibbs energy, L2T-2

P :

total protein in cell, M

Po :

protein per origin, M

S :

stoichiometric matrix

t :

time, T

X :

metabolite concentration, ML-3

YATP/X :

biomass yield coefficient; Z, objective function, T-1

αi :

maximum flux allowable through reaction flux,υ i,T-1

βr :

ribosome activity;μ, specific growth rate, T-1

τ:

doubling time, T

ν :

vector of net conversion rates, T-1

νi :

flux of reactioni, T-1

γs :

degree of reduction

γai :

amount of amino acid over the total amino acid in cell

Ac :

Acetate

AcCoA :

Acetyl coenzyme A

ADPGlc :

ADP-Glucose

ADPHep :

ADP-D-Glycerol-D-mannoheptose

ASPSA :

Aspartate semihaldehyde

C14:0 :

Myristic acid (n-Tetradecanoic)

C14:1 :

β-Hydroxymyristic acid

C16:0 :

Palmitic acid (n-Hexadecanoic)

C16:1 :

Palmitoleic acid (hexa-9-decanoic)

C18:1 :

Oleic Acid

CaP :

Carbamoyl-phosphate

CDP :

Cytidine-5′-diphosphate

CDPDG :

CDP-Diacylglycerol

CDPEtN :

CDP-Ethanolamine

Chor :

Chorismate

Cit :

Citrate

Citr :

Citrulline

CL :

Diphosphatidylglycerol

CMP :

Cytidine-5′-monophosphate

CMPKDO :

CMP-3-Deoxy-D-manno-octulosonic acidCO 2 Carbon dioxide

dADP :

2′-Deoxy-adenosine-5′-diphosphate

dATP :

2′-Deoxy-adenosine-5′-triphosphate

dCDP :

2′-Deoxy-cytidine-5′ -diphosphate

dCTP :

2′ -Deoxy-cytidine-5′ -triphosphate

dGDP :

2′-Deoxy-guanosine-5′-diphosphate

dGTP :

2′-Deoxy-guanosine-5′-triphosphate

DHF :

7,8-Dihydrofolate

dTTP :

2′-Deoxy-thymidine-5′-triphosphate

dUDP :

2′-Deoxy-uridine-5′ -diphosphate

d UTP :

2′ -Deoxy-uridine-5′ -triphosphate

E4P :

Erythrose-4-phosphate

Eth :

Ethanol

F6P :

Fructose-6-phosphate

FADH :

Flavine adenine dinucleotide (reduced)

Form :

Formate

FTHF :

N5-Formimino-tetrahydrofolate

FNTHF :

N10-Formyl-tetrahydrofolate

Fum :

Fumarate

G1P :

Glucose-1-phosphate

G6P :

Glucose-6-phosphate

GDP :

Guanosine-5′-diphosphate

GL :

Glycerol

GL3P :

Glycerol-3-phosphate

Glc :

Glucose

H2S :

Hydrogen sulfide

Hexp :

Protons exported

HSer :

Homoserine

ICit :

Isocitrate

IGP :

Indoleglycerolphosphate

IMP :

Inosinemonophosphate

Lac :

Lactate

LPS :

Lipopolysaccharide

αKG :

α-Ketoglutarate

Kval :

Ketoisovalerate

Mal :

Malate

MalACP :

Malonyl-ACP

mDAP :

meso-Diaminopimelate

MeTHF :

N5, N10-Methenyl-tetrahydrofolate

MetTHF :

N5, N10-Methylene-tetrahydrofolate

MTHF :

N5-Methyl-tetrahydrofolate

NH3 :

Ammonia

OA :

Oxaloacetate

Orn :

Ornithine

PA :

Phosphatidic acid

PE :

Phosphatidyl-ethanolamine

PEP :

Phosphoenolpyruvate

PG :

Phosphatidyl-glycerol

3PG :

Glycerate-3-phosphate

Pi :

Inorganic orthophosphate

PPi :

Inorganic pyrophosphate

PRAIC :

5′ -Phosphoribosyl-4-carboxamide-5-aminoimidazole

ProCoA :

Propionyl-CoA

PRPP :

Phosphoribosylpyrophosphate

PS :

Phosphatidyl-serine

PTRSC :

Putrescine

Pyr :

Pyruvate

Pyrroline :

Δ1Pyrroline-5-carboxylate

QH2 :

Hydroquinone

R5P :

Ribulose-5-phosphate

Rib5P :

Ribose-5-phosphate

S7P :

Sedoheptulose-7-phosphate

SPRMD :

Spermidine

Succ :

Succinate

SuccCoA :

Succinyl coenzyme A

T3P :

Triose-3-phosphate (for glyceraldehyde-3-P and dihydroxyacetone-P)

TREDH :

Thioredoxin (reduced)

UDPNAG :

UDP-N-Acetyl-glucosamine

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  1. Department of Chemical Engineering, University of Manchester Institute of Science and Technology, P. O. Box 88, M60 1QD, Manchester, UK

    Sheau Min See, Jon P. Dean & George Dervakos

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See, S.M., Dean, J.P. & Dervakos, G. On the topological features of optimal metabolic pathway regimes. Appl Biochem Biotechnol 60, 251–301 (1996). https://doi.org/10.1007/BF02783588

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